# Uncertainty-Aware Trajectory Prediction via Rule-Regularized Heteroscedastic Deep Classification

arXiv: https://arxiv.org/abs/2504.13111 · HTML: https://mlsanity.com/paper/2504.13111/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 58 references that are in the map.
- First posted on arXiv 17 Apr 2025.

## Builds on (most cited first, 30 of 44)

- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [nuScenes: A multimodal dataset for autonomous driving](https://mlsanity.com/paper/1903.11027/) (2019)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [Progress & Compress: A scalable framework for continual learning](https://mlsanity.com/paper/1805.06370/) (2018)
- [MultiPath: Multiple Probabilistic Anchor Trajectory Hypotheses for Behavior Prediction](https://mlsanity.com/paper/1910.05449/) (2019)
- [Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness](https://mlsanity.com/paper/2006.10108/) (2020)
- [Learning Lane Graph Representations for Motion Forecasting](https://mlsanity.com/paper/2007.13732/) (2020)
- [Laplace Redux -- Effortless Bayesian Deep Learning](https://mlsanity.com/paper/2106.14806/) (2021)
- [Regularisation of Neural Networks by Enforcing Lipschitz Continuity](https://mlsanity.com/paper/1804.04368/) (2018)
- [DenseTNT: End-to-end Trajectory Prediction from Dense Goal Sets](https://mlsanity.com/paper/2108.09640/) (2021)
- [Motion Transformer with Global Intention Localization and Local Movement Refinement](https://mlsanity.com/paper/2209.13508/) (2022)
- [CoverNet: Multimodal Behavior Prediction using Trajectory Sets](https://mlsanity.com/paper/1911.10298/) (2019)
- [A Survey of Motion Planning and Control Techniques for Self-driving Urban Vehicles](https://mlsanity.com/paper/1604.07446/) (2016)
- [Informed Machine Learning -- A Taxonomy and Survey of Integrating Knowledge into Learning Systems](https://mlsanity.com/paper/1903.12394/) (2019)
- [On Feature Collapse and Deep Kernel Learning for Single Forward Pass Uncertainty](https://mlsanity.com/paper/2102.11409/) (2021)
- [What the Constant Velocity Model Can Teach Us About Pedestrian Motion Prediction](https://mlsanity.com/paper/1903.07933/) (2019)
- [Trajectory Forecasts in Unknown Environments Conditioned on Grid-Based Plans](https://mlsanity.com/paper/2001.00735/) (2020)
- [On the Practicality of Deterministic Epistemic Uncertainty](https://mlsanity.com/paper/2107.00649/) (2021)
- [Generalized Variational Continual Learning](https://mlsanity.com/paper/2011.12328/) (2020)
- [UniTraj: A Unified Framework for Scalable Vehicle Trajectory Prediction](https://mlsanity.com/paper/2403.15098/) (2024)
- [Pre-Train Your Loss: Easy Bayesian Transfer Learning with Informative Priors](https://mlsanity.com/paper/2205.10279/) (2022)
- [Correlated Input-Dependent Label Noise in Large-Scale Image Classification](https://mlsanity.com/paper/2105.10305/) (2021)
- [How many Observations are Enough? Knowledge Distillation for Trajectory Forecasting](https://mlsanity.com/paper/2203.04781/) (2022)
- [The Integration of Prediction and Planning in Deep Learning Automated Driving Systems: A Review](https://mlsanity.com/paper/2308.05731/) (2023)
- [The Importance of Prior Knowledge in Precise Multimodal Prediction](https://mlsanity.com/paper/2006.02636/) (2020)
- [Interpretable Self-Aware Neural Networks for Robust Trajectory Prediction](https://mlsanity.com/paper/2211.08701/) (2022)
- [Beyond Deep Ensembles: A Large-Scale Evaluation of Bayesian Deep Learning under Distribution Shift](https://mlsanity.com/paper/2306.12306/) (2023)
- [Trustworthy Classification through Rank-Based Conformal Prediction Sets](https://mlsanity.com/paper/2407.04407/) (2024)

## Built on by (most cited first, 3 of 3)

- [Heteroscedastic Diffusion for Multi-Agent Trajectory Modeling](https://mlsanity.com/paper/2605.10717/) (2026)
- [Addressing Corner Cases in Autonomous Driving: A World Model-based Approach with Mixture of Experts and LLMs](https://mlsanity.com/paper/2510.21867/) (2025)
- [Uncertainty-Aware Diffusion Model for Multimodal Highway Trajectory Prediction via DDIM Sampling](https://mlsanity.com/paper/2602.21319/) (2026)

## Abstract (arXiv)

Deep learning-based trajectory prediction models have demonstrated promising capabilities in capturing complex interactions. However, their out-of-distribution generalization remains a significant challenge, particularly due to unbalanced data and a lack of enough data and diversity to ensure robustness and calibration. To address this, we propose SHIFT (Spectral Heteroscedastic Informed Forecasting for Trajectories), a novel framework that uniquely combines well-calibrated uncertainty modeling with informative priors derived through automated rule extraction. SHIFT reformulates trajectory prediction as a classification task and employs heteroscedastic spectral-normalized Gaussian processes to effectively disentangle epistemic and aleatoric uncertainties. We learn informative priors from training labels, which are automatically generated from natural language driving rules, such as stop rules and drivability constraints, using a retrieval-augmented generation framework powered by a large language model. Extensive evaluations over the nuScenes dataset, including challenging low-data and cross-location scenarios, demonstrate that SHIFT outperforms state-of-the-art methods, achieving substantial gains in uncertainty calibration and displacement metrics. In particular, our model excels in complex scenarios, such as intersections, where uncertainty is inherently higher. Project page: https://kumarmanas.github.io/SHIFT/.